Assignment2_SolutionsPart1

Assignment2_SolutionsPart1 - BUSI408: CORPORATE FINANCE...

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BUSI408: CORPORATE FINANCE Assignment 2 - Solutions for PART 1 Instructor: Serdar Aldatmaz ____________________________________________________________________________________ _ Chapter 13 7. The expected return of an asset is the sum of the probability of each return occurring times the probability of that return occurring. So, the expected return of each stock asset is: E(R A ) = .15(.05) + .65(.08) + .20(.13) = .0855 or 8.55% E(R B ) = .15(–.17) + .65(.12) + .20(.29) = .1105 or 11.05% To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then add all of these up. The result is the variance. Standard deviation is the square root of the variance. So, the variance and standard deviation of each stock is: σ A 2 =.15(.05 – .0855) 2 + .65(.08 – .0855) 2 + .20(.13 – .0855) 2 = .00060 σ A = (.00060) 1/2 = .0246 or 2.46% σ B 2 =.15(–.17 – .1105) 2 + .65(.12 – .1105) 2 + .20(.29 – .1105) 2 = .01830 σ B = (.01830) 1/2 = .1353 or 13.53% 9. a. To find the expected return of the portfolio, we need to find the return of the portfolio in each state of the economy. This portfolio is a special case since all three assets have the same weight. To find the expected return in an equally weighted portfolio, we can sum the returns of each asset and divide by the number of assets, so the expected return of the portfolio in each state of the economy is: Boom: E(R p ) = (.07 + .15 + .33)/3 = .1833 or 18.33% Bust: E(R p ) = (.13 + .03 - .06)/3 = .0333 or 3.33% To find the expected return of the portfolio, we multiply the return in each state of the economy by the probability of that state occurring, and then sum. Doing this, we find: E(R p ) = .35(.1833) + .65(.0333) = .0858 or 8.58% b. This portfolio does not have an equal weight in each asset. We still need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get: Boom: E(R p ) = .20(.07) +.20(.15) + .60(.33) =.2420 or 24.20% 1
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Bust: E(R p ) = .20(.13) +.20(.03) + .60( - .06) = –.0040 or –0.40% And the expected return of the portfolio is: E(R p ) = .35(.2420) + .65( - .004) = .0821 or 8.21% To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, than add all of these up. The result is the
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Assignment2_SolutionsPart1 - BUSI408: CORPORATE FINANCE...

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